Geometry and symmetries of multi-particle systems

Abstract

The quantum dynamical evolution of atomic and molecular aggregates, from their compact to their fragmented states, is parametrized by a single collective radial parameter. Treating all the remaining particle coordinates in d dimensions democratically, as a set of angles orthogonal to this collective radius or by equivalent variables, bypasses all independent-particle approximations. The invariance of the total kinetic energy under arbitrary d-dimensional transformations which preserve the radial parameter gives rise to novel quantum numbers and ladder operators interconnecting its eigenstates at each value of the radial parameter. We develop the systematics and technology of this approach, introducing the relevant mathematics tutorially, by analogy to the familiar theory of angular momentum in three dimensions. The angular basis functions so obtained are treated in a manifestly coordinate-free manner, thus serving as a flexible generalized basis for carrying out detailed studies of wavefunction evolution in multi-particle systems.

37 pages, 2 eps figures

References in corpus (1)

• The Continuum Structure of the Borromean Halo Nucleus 11Li

Cited by in corpus (8)

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• Energy spectrum of harmonically trapped two-component Fermi gases: Three- and Four-Particle Problem
• Quantum three-body system in D dimensions
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• Quantum Three-Body Problem
• All coordinates transformations that separate the center of mass kinetic energy, their group structure and geometry
• Towards a geometrical classification of statistical conservation laws in turbulent advection
• Non-local divergence-free currents for the account of symmetries in two-dimensional wave scattering